On the construction of copulas and quasi-copulas with given diagonal sections

Nelsen, Roger B.; Quesada-Molina, José Juan; Rodrı́guez-Lallena, José Antonio; Úbeda-Flores, Manuel

doi:10.1016/j.insmatheco.2006.11.011

Cited by 85 publications

(31 citation statements)

References 22 publications

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“…, u) = u for 0 u 1, where −1 is the inverse function of the diagonal section (u) of the copula. Natural applications of the diagonal sections of copulas in the fields of reliability and order statistics can be seen in [18,[26][27][28] and in the references therein.…”

Section: Remark 26mentioning

confidence: 99%

Comparisons of series and parallel systems with components sharing the same copula

Navarro

Spizzichino

2010

Appl Stoch Models Bus & Ind

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SUMMARYThe paper is devoted to study stochastic comparisons of series and parallel systems with vectors of component lifetimes sharing the same copula. We show that, under some conditions on the common copula, the series system with heterogeneous components is worse than the series system with homogeneous components having a common reliability function, which is equal to the average of the reliability functions of the heterogeneous components. However, we show that this property is not necessarily true for arbitrary copulas. We obtain similar properties for parallel systems and for general coherent systems. For these purposes, we introduce in our analysis the notion of the mean function of a copula.

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Section: Remark 26mentioning

confidence: 99%

Comparisons of series and parallel systems with components sharing the same copula

Navarro

Spizzichino

2010

Appl Stoch Models Bus & Ind

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“…Γ = {(x, x) | x ∈ I}: see (Durante et al, 2007a;Nelsen et al, 2008). Moreover, it also applies to all the cases where two copulas A and A coincides on a given Γ being the graph of a continuous and strictly increasing function of I.…”

Section: Patchwork Of Copulasmentioning

confidence: 99%

A New Characterization of Bivariate Copulas

Durante

Jaworski

2010

Communications in Statistics - Theory and Methods

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“…Recent advances in mathematics show that the copula-based techniques [17,20] could be provided as an efficient mathematical tool for the multivariate analysis problem. A copula is a multivariate distribution function of a random vector with uniform marginal distributions in (0,1), which decouples the marginal CDFs and the joint CDF.…”

Section: System Probability Of Failure Estimation With Copulas and Namentioning

confidence: 99%

The probabilistic analysis and optimal design of a bevel gear transmission system with failure interaction

Lü

Zhencai

2017

EiN

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Article citation info: IntroductionGenerally, multiple failure modes may occur in a gear transmission system. Due to the common-source of the input random variables of the system, such as the external loads, the geometric parameters and the material properties, the existing failure modes would be correlated to a certain extend [2,13]. From another perspective, it means that a failure may cause another failure occurs more rapidly, or just the opposite. Actually, whether the dependence of different failure modes is considered during the reliability design process may affect the system reliability estimation greatly. The commonly used independent assumption between failure modes usually leads to defects in gear HAO L, ZHENCAI Z. The probabilistic analysis and optimal design of a bevel gear transmission system with failure interaction. Eksploatacja i Niezawodnosc -Maintenance and Reliability 2017; 19 (2): 220-228, http://dx.doi.org/10.17531/ein.2017.2.9. Lu HAO Zhu ZHENCAIThe probabilisTic analysis and opTimal design of a bevel gear Transmission sysTem wiTh failure inTeracTion probabilisTyczna analiza i opTymalne projekTowanie układu przekładni sTożkowej z uwzględnieniem inTerakcji między uszkodzeniami

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On the construction of copulas and quasi-copulas with given diagonal sections

Cited by 85 publications

References 22 publications

Comparisons of series and parallel systems with components sharing the same copula

Comparisons of series and parallel systems with components sharing the same copula

A New Characterization of Bivariate Copulas

The probabilistic analysis and optimal design of a bevel gear transmission system with failure interaction

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